Good question.
It adds the ability to override configurations via .htaccess or virtual host configuration, just like Apache's mod_php. It is a major security concern to use PHP with Fast CGI SAPI under shared hosting environment.

how should it work then?
You talk about performance advantages but litespeed is a single-process webserver.
doesn't the php still need to run in multiple separate processes so that it will be running kind of like with fast-cgi?

Yes, it works in similiar way as Fast CGI SAPI.
Cannot call any code that causes blocking inside a non-blocking event driven application.
And I don't want to run PHP in another thread, as PHP is not very thread friendly and I don't want the whole server crash with PHP. ;-)

There is one environment variable can be used to customize PHP LiteSpeed application. PHP_LSAPI_MAX_REQUESTS=XXXX controls how many requests each child process will handle before exit. It protects against memory leak inside PHP. Default value is 500.

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What about "PHP_FCGI_CHILDREN=XX" ?
Is there an option like that for lsapi or is it handled differently? How?

How does that work with php-caches like eaccelerator or mmcache?
I've had problems with them if the php-processes are spawned depending on the load which would lead to multiple php-instances not controlled by one php-process.
The php-caches would have their own separate shm-segment for each php-instance which doesn't make too much sense.
Your architecture *sounds* like it would produce the same result. Or do php-caches even work with it?